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On the Hausdorff dimension of general Cantor sets

Published online by Cambridge University Press:  24 October 2008

A. F. Beardon
A. F. Beardon
Affiliation:
Imperial College, London
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Extract

Introduction and notation. In this paper a generalization of the Cantor set is discussed. Upper and lower estimates of the Hausdorff dimension of such a set are obtained and, in particular, it is shown that the Hausdorff dimension is always positive and less than that of the underlying space. The concept of local dimension at a point is introduced and studied as a function of that point.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 61 , Issue 3 , July 1965 , pp. 679 - 694
Copyright
Copyright © Cambridge Philosophical Society 1965

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